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3 years ago

What is the area of the figure? 40 ft2 84 ft2 96 ft2 can't be determined

Mathematics

1 answer:

maxonik [38]3 years ago

5 0

<span>80 ft^2 Looking at the figure, you can easily determine that it's made of two separate figures, a rectangle that's 2 feet by 16 feet, and a triangle that has sides of 16 feet, 10 feet, and 10 feet. The triangle can then be divided into two right triangles with a hypotenuse of 10 feet and one leg of 8 feet, so you can use the Pythagorean theorem to calculate the other leg (which is also the height of the large triangle mentioned above). That value is sqrt(10^2 - 8^2) = sqrt(100 - 64) = sqrt(36) = 6. So we now know that the large 16,10,10 triangle has a base of 16 and a height of 6. So let's calculate the area of the entire figure. A = 2*16 + 16*6/2 A = 32 + 16*3 A = 32 + 48 A = 80 So the area of the entire figure is 80 square feet.</span>

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Answer: $3\leq x \leq 18$

Step-by-step explanation:

Given, the length of the rectangular dog run is 18 feet.

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$42\leq 2 (x+18)\leq 72$

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Subtract 18 from each side, we get

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The base of a triangle is 3 more than 2 times of height. Determine the dimensions that give total area of 10 square feet.

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Answer:

height = 2.5 ft , base = 8 ft

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = $\frac{1}{2}$ bh ( b is the base and h the height )

height = h then base = 2h + 3 and A = 10 , then

$\frac{1}{2}$ h(h + 3) = 10 ( multiply both sides by 2 to clear the fraction )

h(h + 3) = 20 , that is

h² + 3h = 20 ( subtract 20 from both sides )

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h + 4 = 0 ⇒ h = - 4

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but h > 0 , then h = 2.5

and 2h + 3 = 2(2.5) + 3 = 5 + 3 = 8

that is height = 2.5 ft and base = 8 ft

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